Question

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

score 240 · Answer 1 · 2026-05-07 18:27:05

240

Views

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

Published on 07 May 2026 - 18:27

score 923 · Answer 2 · 2026-04-20 16:31:31

923

Views

How is symmetry in an inequality determined?

Published on 20 Apr 2026 - 16:31

score 184 · Answer 3 · 2026-05-02 20:21:34

184

Views

Does $(\sum_{i=1}^n a_i^{1.5})^2 - \sum_{i=1}^n a_i \; \sum_{i=1}^n a_i a_{i+1} > 0$ hold for $n \leq 8$?

Published on 02 May 2026 - 20:21

score 87 · Answer 4 · 2026-04-29 12:51:50

87

Views

Generalization of the Pólya–Szegő inequality

Published on 29 Apr 2026 - 12:51

score 156 · Answer 5 · 2026-04-29 12:52:04

156

Views

Is it true that $\frac {a}{a+b}+\frac {b}{b+c}+\frac {c}{c+a}\geq \frac32$ if $a+b+c=1$?

Published on 29 Apr 2026 - 12:52

score 178 · Answer 6 · 2026-05-03 08:58:12

178

Views

How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Published on 03 May 2026 - 8:58

score 70 · Answer 7 · 2026-04-29 12:51:44

70

Views

Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Published on 29 Apr 2026 - 12:51

score 78 · Answer 8 · 2026-04-29 12:51:50

78

Views

Show that problem and that equality if fulfilled iff a=b

Published on 29 Apr 2026 - 12:51

score 193 · Answer 9 · 2026-05-06 17:14:16

193

Views

replacing Inequalities

Published on 06 May 2026 - 17:14

score 399 · Answer 10 · 2026-04-29 12:51:23

399

Views

Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

Published on 29 Apr 2026 - 12:51

score 151 · Answer 11 · 2026-04-29 12:51:28

151

Views

Show that $a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}$ holds for $a,b,c>0$

Published on 29 Apr 2026 - 12:51

score 450 · Answer 12 · 2026-05-10 13:28:11

450

Views

Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Published on 10 May 2026 - 13:28

score 107 · Answer 13 · 2026-05-10 13:24:04

107

Views

Application of Chebyschev inequality

Published on 10 May 2026 - 13:24

score 81 · Answer 14 · 2026-05-10 13:25:07

81

Views

Optimization of sum of squares over permutations

Published on 10 May 2026 - 13:25

score 88 · Answer 15 · 2026-05-10 13:24:10

88

Views

How does the number $3$ help in this (probably Cauchy-based) inequality?

Published on 10 May 2026 - 13:24

List Question

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

How is symmetry in an inequality determined?

Does $(\sum_{i=1}^n a_i^{1.5})^2 - \sum_{i=1}^n a_i \; \sum_{i=1}^n a_i a_{i+1} > 0$ hold for $n \leq 8$?

Generalization of the Pólya–Szegő inequality

Is it true that $\frac {a}{a+b}+\frac {b}{b+c}+\frac {c}{c+a}\geq \frac32$ if $a+b+c=1$?

How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Show that problem and that equality if fulfilled iff a=b

replacing Inequalities

Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

Show that $a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}$ holds for $a,b,c>0$

Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Application of Chebyschev inequality

Optimization of sum of squares over permutations

How does the number $3$ help in this (probably Cauchy-based) inequality?

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